Hello,
I just finished reading The Kuzari - The Principle and the Formalism by David Yust and it was indeed a very well thought out piece except for the lack of two very important underlying premises.
The Kuzari Principle relies on the cultural pressures and probabilities inherent in early Judaism for it's veracity of eye witness accounts of supernatural events being transmitted to successive generations and the Objective Reason responder has no such pressures or obligation to veracity.
The main premise of the Jewish argument lies in the fact that by their very own superstitions and rules they have insured the reliability of their information unlike any other religious group before or since. The penalty for falsely relating information about any event involving their Creator Being was death and the theme of Jews choosing death over compromise in regards to their accounts of religious events is well documented. This places the likelihood that they would fabricate a mythology in some pretty remote territory.
There has been an document able unbroken line of transmission about these stories from Torah at least from the time of the Pre-Christian Qumran documents until present day and given the fact that their own beliefs prevent them from fabricating them under penalty of certain death for much of that time leaves me to ask if a similar claim of veracity(under threat of death) can be made for the Rational Responders who has no sense of absolute morality and no self or culturally imposed restrictions hanging over their collective heads.
Christians, Muslims, etc all have a sense of absolute morality but it's in a far off lofty imagined afterlife where they will pay for what they do in the world today but the Jews of antiquity would be risking their very lives by merely embellishing a story in the presence of other Jews.
So the Kuzari Principle depends on an absolute sense of morality and honesty(backed by the threat of certain death) while the modern critic "picks and chooses" his/her morality and ethics on a whim so who's argument is more likely to be true?
The Kuzari Principal is not a series of rational proofs that can be applied to any idea but one that only has a concrete point when used in the context of people who can arguably be proven to be very honest and not through some self asserted form of propaganda but through social and cultural mechanisms that reduced the possibility of dishonesty to almost nothing.
[continued]

1. Aristotelian gravity should have produced expected evidence (heavier masses accelerating toward the earth faster than lighter masses) which were absent. & Aristotelian gravity was refuted before the actual experiment in a thought experiment (if you attach two balls together by a chain, when they would become tight, they should excelerate (being a total greater weight), which is absurd.

The US engages in a known conspiracy including falsified weather radar reports, post office redirection of letters, appearances at malls.

At #2, we have a clear case of a parallel to the miracle of the manna concocted for cultural gain.

What gain could a nation of parents have in promoting a religion to their children?
The same.

3. The bible itself claims that knowledge of God was lost and so the chain of oral tradition was broken:

Judges 2
10 After that whole generation had been gathered to their fathers, another generation grew up, who knew neither the LORD nor what he had done for Israel.

4. It is problematic that the Kuzari example is itself not sanctioned by tradition. You do not find it taught to the Orthodox (other than by Rabbi Gottlieb) as a *basis* for belief, at all. Orthodox Judaism does not set itself up to such a test, such that if it failed, it would surrender.

5. The Kuzari argument is a classic argument from ignorance: We do not conclude about the nuclear force anything more than what we can verify.

5b. There can be a force, but that does not justify / sanction specifically the Torah in toto.

6. In the Traditional is the belief that the world is actually less than 6000 years old (missing evidence: starlight only 6K, an earth only 6K ... That says something about our ability to believe anything.

7. The problem with the Kuzari principle is that it requires not only
1. satisfying the principle, but the geometrically more difficult step of
2. FINDING a counter example.

There may be examples out there, but *knowing* they are false beliefs requires a super position nobody claims to have.

The absense of evidence yeilds (only?) cases where we can not *know* that they were false.

Let's try to find a counter-example to the Manna:

Other cases:

They believe(d) X.
X should have produced evidence Y.
(end of Manna parallel)

We now know X did not occur because...?

If Y is missing, how can we - today - conclude that they were *wrong*?

Put another way, if there are other historical cases where evidence should have been produced, but was not, we now have no way to know that it was false.

We have no way to produce counter examples at all, by definition, we can only look at historical examples where there is no evidence. So we are limitted to cases where we can not know. There could be hundreds of cases.